What does "lose face" mean?

[Marinka]

English Idioms and Expressions, Advanced Level

ESL/EFL Test #11 "Losing It", question 1

The one thing a public figure hates is when he loses face in front of all his admirers.

(a) loses good looks
(b) loses photos
(c) loses respect
(d) loses expressions

English Idioms and Expressions, Advanced Level

ESL/EFL Test #11 "Losing It", answer 1

The one thing a public figure hates is when he loses respect in front of all his admirers.

Correct answer: (c) loses respect
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i dont know what a meaning "loses face" can you help me?

Marinka

[Yankee]

Hi Marinka

When you lose face, you suffer disgrace, humiliation, or embarrassment: It was impossible to apologize publicly without losing face.
(See definition 49 here)

Or, as the answer to the test says, you lose the respect of others.

Amy